In general relativity, freely-falling objects follow geodesics of the background spacetime in which they live. In a sense, this feature is a mere rephrasing of Einstein’s equivalence principle.
In 1968, Brandon Carter showed that the geodesic motion of objects orbiting a Kerr black hole was integrable, in the sense of Hamiltonian mechanics, by discovering a fourth constant of motion that now bears his name. This “universality” of geodesic free fall, however, is but an approximation : In general, two different bodies will follow two distinct paths, depending on how they spin and deform. In this talk, I will show how, and to which extent, Carter’s integrability of Kerr geodesics can be extended to the motion of not just mere point masses, but also extended bodies that can spin and deform.